We compare the collective modes for Bose-condensed systems with two
degenerate components with and without intercomponent coherence at
finite temperature using the time-dependent Hartree-Fock
approximation. We show that the interaction between the condensate
and non-condensate in these two cases results in qualitatively
different collective excitation spectra. We show that at zero
temperature the single-particle excitations of the incoherent Bose
condensate can be probed by intercomponent excitations. [Preview Abstract]

When two classical shock waves collide, the interaction is
relatively simple and is explained by classical hyperbolic system
theory and jump/entropy conditions. An analogous theory for the
interaction of two dispersive shock waves (DSWs) is presented.
Two cases will be considered: i) a collision where two DSWs are
propagating directly toward one another, ii) merging where a
faster DSW overtakes a slower one. It is shown that, after a
complicated quasi-periodic or multi-phase region is created, the
DSW interaction process results in: i) two single DSWs
propagating away from one another in the collision case, ii) a
single, larger DSW representing the merger of the original two
DSWs in the merging case. Remarkably, these results coincide
exactly with their classical shock wave counterpart. These
results have direct application to Bose-Einstein condensates and
nonlinear optics. [Preview Abstract]

We report our study of the effects of disorder on a Bose-Einstein
condensate (BEC)
of $^7$Li atoms with tunable interaction. A large $^7$Li BEC is
created in an
elongated optical trap after forced evaporation.
The strength of the repulsive interaction is tuned using a
magnetic Feshbach
resonance. A disordered optical potential, whose strength is
also tunable, is
generated by projecting a laser speckle pattern onto the atoms.
We have
performed transport studies by measuring the center of mass
motion of the trapped
BEC in the presence of disorder. Beyond a disorder strength
($V_t$), the dipole
oscillation of the superfluid BEC is completely suppressed,
signaling a transition to
an insulator. We have also studied the time of flight expansion
of the BEC after
release from the trap and disordered potentials. With
intermediate disorder
strengths, striking fringes appear in the cloud after sufficient
expansion time.
Beyond some disorder strength ($V_p$), comparable to the chemical
potential of the
trapped BEC, the fringes are washed out, signaling a loss of
phase coherence.
Interestingly, $V_p$ is significantly larger than $V_t$,
suggesting that finite phase
coherence can still exist in the insulator. [Preview Abstract]

The quantum delta kicked accelerator can be realized by
subjecting cold atoms to spatially corrugated off resonant
pulses of light. These standing wave pulses are applied in the
direction in which there is a component of gravity and result in
acceleration of a group of atoms. For the first time we observed
Quantum Accelerator Modes (QAM) in BEC. We show that using
the narrow momentum distribution of BEC, the structures in phase
space map produced by a psuedo classical theory can be directly
studied. We show that QAMs can be effeciently populated using
BEC. Details will be presented. [Preview Abstract]

We have studied the density distribution of binary mixtures of
$^{87}$Rb and $^{85}$Rb Bose--Einstein condensates under
conditions similar to a recent experiment conducted in the Jin
Group at JILA. In this experiment, a binary mixture of the two
Rb isotopes were confined in a magnetic trap and rf evaporative
cooling was carried out on the $^{87}$Rb causing sympathetic
cooling of the $^{85}$Rb. This mixture was then transferred to
an optical trap to minimize $^{85}$Rb 3--body loss and
condensation was achieved by slowly decreasing the depth of the
optical trap. An external magnetic field using a Feshbach resonance
enabled tuning of the 85--85 scattering length. Density profiles
were obtained by taking absorption images of expanded condensates
after releasing them from the trap. We have calculated the
theoretical shape of such images by solving approximately the
coupled time--dependent (TD) Gross--Pitaevskii (GP) equations.
As initial states we used Thomas--Fermi approximate solutions of
the time--independent GP equation and approximately solved the
time--dependent Gross--Pitaevskii equation to model the
expansion. We present a comparison of this calcualation with the
experimental data. [Preview Abstract]

We examine Bose-Einstein spinor condensates in the short-time
non-linear regime for S=1 atoms in the context of $^{87}$Rb
studied experimentally by the Stamper-Kurn group [L. Sadler et
al, Nature {\bf 443}, p193, 2006]. We will describe the
quantum dynamics of a sample that starts as a condensate of $N$
atoms in a pure $S=1$, $m_f=0$ state. Our approach seeks to
improve the mean-field description of such systems by including
the contributions of quantum fluctuations that seed the eventual
formation of ferromagnetic domains. We will give a simple
quantum description of the system for the short-time regime in
analogy with ``two-mode squeezing" of quantum optics, treating
the initial $m_f=0$ condensate as a source for the conversion to
pairs of $m_f=1,-1$ states. Even though the system as a whole
is described by a pure state with zero entropy, the reduced
density matrix for the $m_f=+1$ degree of freedom, obtained by
tracing out the $m_f=-1,0$ degrees of freedom, is a thermal
state. We propose to observe the large fluctuations associated
with this thermal state using Hanbury-Brown-Twiss noise
correlation measurements in the density and momentum
distributions of the individual $m_f$ species. Finally, we will
discuss the effect of excitations in connection to the seeding
and ultimate formation of domains of ferromagnetically aligned
spins. (Supported by NSF DMR-0603369). [Preview Abstract]

Bose-Einstein condensates are quantum fluids governed by nonlinear
interatomic interactions. They provide an excellent tool to study intriguing
phenomena in the field of nonlinear hydrodynamics. We will report on
hydrodynamics experiments carried out in a newly constructed BEC apparatus
at Washington State University, Pullman. Current research directions include
quantum shock waves and parametric resonances. We will describe the current
results and future directions. [Preview Abstract]

The Bogoiubov-de Gennes equations are used for a number of
theoretical
works on the trapped Bose-Einsetein condensates. Particularly,
it is
important that if all of the eigenvalues of the equations are
real, the
solutions of the equations diagonalize the unperturbed
Hamiltonian, and
the quasi-particle picture, which describes the quantum
fluctuation
around
the condensates, is obtained. We consider the quantum
fluctuation in the case that these equations have complex
eigenvalues.
First, to expand quantum field which represents the quantum
fluctuation,
we give the complete set including pairs of complex modes whose
eigenvalues are complex conjugate to each other. The expansion
of the
quantum field brings the operators associated with the complex
modes,
which are simply neither bosonic nor fermionic ones. Next, to
evaluate
physical quantities, we construct the eigenstate of the complex
mode
sector of the unperturbed Hamiltonian. Finally, we discuss the
instability of the condensates caused by the quantum fluctuation
associated with the complex mode in the context of Kubo's linear
response theory. [Preview Abstract]

We study formations of heteronuclear Feshbach molecule
in population imbalanced atomic gases, extending the recent work
[J. E. Williams et. al., New J. Phys. 8, 150 (2006)] on the
Feshbach molecule formation. We find that conversion efficiency
depends on
a ratio of the number of atomic species in the initial state
before the
magnetic sweep, as well as an initial temperature and an initial
peak phase
space density. At low temperature in quantum degenerate regime,
quantum
statistics of atoms plays an important role in conversion
efficiencies.
Maximum conversion efficiencies are determined by quantum
statistics and the
number ratio. When the major component is bosonic, the maximum
conversion
efficiency is $50\%$. On the other hand, when the major component is
fermionic and the minor component is bosonic, the maximum conversion
efficiency has a range from $50\%$ to $100\%$, which is
determined by the
initial atomic ratio. In the case that both components are fermionic,
the maximum conversion efficiency is $100\%$. In the region where
the gases
does not condense, the conversion efficiency is described as a
function of
initial peak phase space density of a major component. [Preview Abstract]

Gaussian distribution is commonly used as a good approximation to
study the trapped one-component Bose-condensed atoms with
relatively small nonlinear effect. It is not adequate in dealing
with the one-component system of large nonlinear effect, nor the
two-component system where phase separation exists. We propose a
modified Gaussian distribution which is more effective when
dealing with the one-component system with relatively large
nonlinear terms as well as the two-component system. The modified
Gaussian is also used to study the breathing modes of the
two-component system, which shows a drastic change in the mode
dispersion at the occurrence of the phase separation. The results
obtained are in agreement with other numerical results. [Preview Abstract]

Using path integral Monte Carlo simulation methods[1], we have
studied
properties of impurities immersed in Bose-Einstein Condensates
harmonically
trapped in low dimemsion. For two-body interactions,
we use a hard-sphere potential
whose core radius equals its corresponding scattering length. We
assume that
the impurities experience the external trapping potential.
We have tightly confined the motion of trapped particles
in one or more direction by increasing the trap anisotropy
in order to simulate lower dimensional atomic gases.
By varying the strength of the boson-impurity interactions and
the number of
impurities, we have investigated the effect of impurities on
the energetics and structural properties such as the total energy,
the density profile, and the superfluid fraction. Our results
show that
for impurities with larger two-body interactions than
the boson-boson interactions,
the impurities move away from the trap center and surround the
trapped bosons,
and the density profile is found to get narrower, with the peak
density
getting larger. The total superfluid fraction decreases due to
the impurities,
although the difference becomes smaller and smaller by increasing
the trap anisotropy.
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\noindent
*Research supported by NASA\\
\noindent
[1] K.~Nho and D.~P.~Landau, Phys. Rev. A. {\bf 72}, 023615 (2005). [Preview Abstract]

We have studied the expansion of a mixture of $^{85}$Rb--$^{87}
$Rb Bose--Einstein condensates within the Thomas--Fermi
approximation. Systems involving mixtures of Bose--Einstein
condensates of different atomic species can be accurately
modeled by coupled Gross--Pitaevskii equations. As for single
condensates, the coupled Gross--Pitaevskii equations can be
written in hydrodynamic form where each condensate is described
by a density and phase. Also just as for single condensates,
the hydrodynamic equations of motion for condensate mixtures
reduce to classical equations of motion when their quantum
pressure terms are neglected (Thomas--Fermi approximation). In
this case, it is possible to find time--dependent Thomas--Fermi
approximate solutions for the hydrodynamic equations of motion
for mixtures. We present these equations and their solution for
the particular case of a $^{85}$Rb--$^{87}$Rb expansion that
occured in a recent experiment performed in the Jin group at
JILA. We also highlight interesting features that can occur
because of interaction effects in the expansion of multiple--
condensate mixtures. [Preview Abstract]